Do these vulnerabilities impact a local ntpd instance responsible only for local timekeeping? (In other words, does a compromised machine in pool.ntp.org pose a threat?)
#1 Weak default key in config_auth()
If you're only doing local timekeeping, and not using authentication (you'd know if you were) this doesn't apply. Basically the automatically generated key used for authentication (if you didn't specify one) was only 31 bits long and easily guessable.
#2 non-cryptographic random number generator with weak seed used by ntp-keygen to generate symmetric keys
Same as the above. If you're not using keyed sessions with remote hosts, this doesn't apply to you. Even if you are, the worst you're losing here is that someone could potentially mess with your clock.
#3 Buffer overflow in crypto_recv()
If you are using crypto (i.e. your ntp.conf file contains a line starting with "crypto pw"), you are potentially remotely exploitable to remote code execution. You probably do not have that configuration line set unless you know you put it there.
#4 Buffer overflow in ctl_putdata()
From the sound of the post on ntp.org, this is the scary one. "A remote attacker can send a carefully crafted packet that can overflow a stack buffer and potentially allow malicious code to be executed with the privilege level of the ntpd process." This makes it sound like everyone is exploitable. However, Redhat says "the ctl_putdata() flaw, by default, can only be exploited via local attackers". This makes me believe if you have your ntp.conf locked down using the 'restrict' lines you might not be vulnerable.
#5 Buffer overflow in configure()
This is the same as #4, ntp.org's advisory is vague enough that it sounds like everyone is vulnerable. Redhat is saying "the configure() flaw requires additional authentication to exploit." I do not know what this means.
#6 receive(): missing return on error
From their description, it's technically possible (but they haven't done it) to get ntpd into a weird state that is unlikely to be exploitable.
TL;DR: You're possibly vulnerable to #4 and #5 on a stock configuration. Redhat says no, ntp.org's advisory is vague enough that I'm not sure.
Does it affect any ntpd asking for time?
Does it affect a ntpd asking a compromised server for time?
Does it only affect ntpds answering to time requests?